Quiz 1

SOC 221 | Summer 2025

Now that you’ve had the opportunity to discuss with a classmate/classmates how you approached each problem (and your answers), let’s go over each question as a class.

Before we work through how to do each problem, submit your most recent answer and corresponding confidence assessment.

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PART A: Fill in the blank


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


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The class distributions for the answer and associated confidence levels are shown below. Correct answers are shown in orange and your answer/selection is shown via dashed black line.





Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


Answer


You can find the total N of this sample by looking at the last row of the cumulative frequency column (Cf) or by adding up the entire frequency column (f):


22 + 43 + 66 + 51 + 14 + 4 + 2 = 202

PART A: Fill in the blank


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


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The class distributions for the answer and associated confidence levels are shown below. Correct answers are shown in orange and your answer/selection is shown via dashed black line.





Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


Answer


You can find this cumulative frequency by looking at the row of the cumulative frequency column (Cf) associated with 4 hours or less of television or by adding up the frequency column (f) for values 0, 2, 3, and 4:


22 + 43 + 66 + 51 = 182


PART A: Fill in the blank


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


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The class distributions for the answer and associated confidence levels are shown below. Correct answers are shown in orange and your answer/selection is shown via dashed black line.





Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


Answer


You can find this cumulative percentage by looking at the row of the cumulative percentage column (C%) associated with 6 hours or less of television or by adding up the % column (%) for values 0, 2, 3, 4, 5, and 6:


10.89 + 21.29 + 32.67 + 25.25 + 6.93 + 1.98 = 99.01


PART A: Fill in the blank


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


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The class distributions for the answer and associated confidence levels are shown below. Correct answers are shown in orange and your answer/selection is shown via dashed black line.





Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


Answer


You can find this cumulative percentage by adding up the % column (%) for values 4, 5, 6, and 12:


25.25 + 6.93 + 1.98 + 0.99 = 35.15

or by subtracting the cumulative percentage column for 3 hours or less from 100%:


100 - 64.85 = 35.15


PART A: Fill in the blank


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


  1. Calculate the following measures of central tendency to describe the number of hours of TV watched.
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The class distributions for the answer and associated confidence levels are shown below. Correct answers are shown in orange and your answer/selection is shown via dashed black line.





Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


Answer


Calculate the mean:


\frac{(0*22) + (2*43) + (3*66) + (4*51) + (5*14) + (6*4) + (12*2)}{202} = \frac{606}{202} = 3


We can find the median by looking for which value contains the 50th percentile:


3\text{ hours} = 32.19\% - 64.85\%


The mode will be the row that contains the largest frequency (f) / percentage (%):

3\text{ hours} = 66 = 32.67\%

PART A: Fill in the blank


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


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Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


Answer


The distribution appears to be SYMMETRICAL since:

  • the mean, median, and mode are all the same
  • the frequency distribution shows high level of clustering with few big outliers


PART A: Fill in the blank


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


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*


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


Answer


Since the variable is measured at the interval level, mean is generally preferable given that it considers the most information. [and there is no indication that the use of the mean provides a misleading picture of central tendency].


PART A: Fill in the blank


Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


  1. Calculate the following measures of variability for the amount of TV watched.
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The class distributions for the answer and associated confidence levels are shown below. Correct answers are shown in orange and your answer/selection is shown via dashed black line.





Professor Iwannatenure is interested in studying how television exposure affects Americans’ social attitudes. Given limited resources, the good professor will rely on information collected from a sample of American adults to draw her conclusions. She starts by examining the number of hours of TV watched by this group of adults per day, summarizing the distribution in the following frequency table.

# of Hours f % Cf C%
0 22 10.89 22.00 10.89
2 43 21.29 65.00 32.18
3 66 32.67 131.00 64.85
4 51 25.25 182.00 90.10
5 14 6.93 196.00 97.03
6 4 1.98 200.00 99.01
12 2 0.99 202 100


Answer

Calculate the range:


12-0 = 12


Calculate the standard deviation:


\sqrt{\frac{[(0-3)^2*22] + [(2-3)^2 * 43] + [(3-3)^2 * 66] + [(4-3)^2 * 51] + [(5-3)^2 * 14] + [(6-3)^2 * 4] + [(12-3)^2 * 2]}{202 - 1}} =

\sqrt{\frac{[9 *22] + [1 * 43] + [0 * 66] + [1 * 51] + [4 * 14] + [9 * 4] + [81 * 2]}{201}} =

\sqrt{\frac{198 + 43 + 0 + 51 + 56 + 36 + 162}{201}} =

\sqrt{\frac{546}{201}} =


\sqrt{2.716418} = 1.648156 \text{ or} \approx 1.648


PART A: Fill in the blank


  1. For the sake of comparison, Professor Iwannatenure compares her data on adults to data from a large sample of children. The descriptive statistics for the number of hours of TV watched by the sample of children look like this:


\hspace{1cm}\bar{X} = 5.5\hspace{1cm}Median = 3.5\hspace{1cm}Mode = 3.0\hspace{1cm}Range = 20\hspace{1cm}s_X = 2.8


Using this information and the statistics you calculated above, describe how the adults compare to the children in terms of the amount of TV watched and in terms of the diversity of the amount of TV watched. Refer to the specific numbers you use to reach your conclusions.


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  1. For the sake of comparison, Professor Iwannatenure compares her data on adults to data from a large sample of children. The descriptive statistics for the number of hours of TV watched by the sample of children look like this:


\hspace{1cm}\bar{X} = 5.5\hspace{1cm}Median = 3.5\hspace{1cm}Mode = 3.0\hspace{1cm}Range = 20\hspace{1cm}s_X = 2.8


Using this information and the statistics you calculated above, describe how the adults compare to the children in terms of the amount of TV watched and in terms of the diversity of the amount of TV watched. Refer to the specific numbers you use to reach your conclusions.


Mean and median (safer to use since children’s distribution seems to be skewed) are higher for children than adults indicating a higher amount of TV watching among children.


The range and standard deviation are both higher for children than for adults indicating more diversity among children.


PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



PART B: Multiple Choice


For the last two questions, use the standard normal table or a z-score calculator and consider the following: the distribution of heights for men is normally distributed with a mean of 70 inches and a standard deviation of 4 inches.


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



If we plug the numbers we know into the z score calculator we can see that the probability of being 76 inches or taller is:


\approx 0.066807 \text{ or } 6.68\%


PART B: Multiple Choice


For the last two questions, use the standard normal table or a z-score calculator and consider the following: the distribution of heights for men is normally distributed with a mean of 70 inches and a standard deviation of 4 inches.


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Below is a joint distribution of the class’ answers and associated confidence levels. Darker colors denote a greater joint frequency. The correct answer is shown in orange and your answer is labeled.



We know that a z-score of 1.96 on either side of the standardized normal distribution mean of 0 is going to equal 95% of the distribution. Therefore, we just need to solve our equation for X instead of z:


X = \mu + z\sigma

X = 70 \pm 1.96(4)

X = 70 \pm 7.84

X = 70 \pm 7.84

X = 62.16 - 77.84


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